I don't think killing animals senselessly is a good thing.
The rat was looking to increase its territory, food supply, and in the process spread feces, reproduce, and destroy Mem's lair. In a strict animal-on-animal basis, the rat was looking to gain at Mem's expense. Any animal doing that to another without which it has a symbiotic relationship, is creating a confrontation that usually results in a fight or death for one or the other animal. Rats have the advantage of numbers, heightened senses, sharp teeth, and industrial strength constitutions. Mem has the advantage of having a reasoning brain, specialized social support, and opposable thumbs. He also has better vision. The rat used stealth, Mem used his brain, assistance from other humans (who designed, marketed, and sold him the trap), and his opposable thumbs. The rat lost.
That's how it works in the world when one animal encounters another. There's nothing special about us when it comes to these one-on-one, unprovoked (in that Mem didn't go looking to hunt or invite rats into his den), confrontations. Like any other animal, we defend our dens and resources from other animals.